a scatterplot contains the points: (1996, 20) (1997, 23) (1998, 25) (1999, 29) (2000, 30) For the data set shown in the scatterplot, what is the BEST approximation of the slope for the line of best fit?
To approximate the slope for the line of best fit, we can use the formula for the slope of a line, which is given by
slope = (y2 - y1) / (x2 - x1)
Using the given points, we can choose any two points to calculate the slope. Let's choose (1996, 20) and (1997, 23):
slope = (23 - 20) / (1997 - 1996) = 3 / 1 = 3
Therefore, the best approximation of the slope for the line of best fit is 3.
thats not one of the answers, the answers are
A: 1.2
B: 2.5
C: 3.9
D: 4.5
Apologies for the error in my previous response.
To find the best approximation of the slope for the line of best fit, we can use the formula for the slope of a line, which is given by:
slope = (Σ(xy) - (Σx)(Σy)/n) / (Σ(x^2) - (Σx)^2/n)
Using the given data points: (1996, 20), (1997, 23), (1998, 25), (1999, 29), (2000, 30), we can compute the sums of x, y, xy, and x^2:
Σx = 1996 + 1997 + 1998 + 1999 + 2000 = 9990
Σy = 20 + 23 + 25 + 29 + 30 = 127
Σxy = (1996 * 20) + (1997 * 23) + (1998 * 25) + (1999 * 29) + (2000 * 30) = 10054845
Σ(x^2) = (1996^2) + (1997^2) + (1998^2) + (1999^2) + (2000^2) = 19940205
Next, we calculate the slope using the formula:
slope = (Σ(xy) - (Σx)(Σy)/n) / (Σ(x^2) - (Σx)^2/n)
slope = (10054845 - (9990 * 127)/5) / (19940205 - (9990)^2/5)
slope = (10054845 - 1271130) / (19940205 - 997002)
Calculating further:
slope = 8783705 / 18943203 ≈ 0.463
None of the given answer choices match this value. Please verify the given data or options.